A floor tile in the shape of a rhombus has sides of 52 cm and a diagonal of the length 48 cm. Find
i.) the length of the other diagonal
ii.) the area
Answers
Answer❣
Given
Perimeter of Rectangle is 60m
length is 4m more than four times it's breadth
To Find
length and breadth of the Rectangle
Solution
Let us assume the breadth of Rectangle be 'x'
according to the question
length would be => 4m+4x
Perimeter is 60m
Perimeter of Rectangle=2(length+Breadth)
=>60= 2( 4+4x +x)
=>60=2(4+5x)
=>2(4+5x)=60
=>4+5x=30
=>5x= 30-4
=>5x= 26
=>x= 26÷ 5
=>x=5.2
Now , breadth is 5.2m
length = 4+4x=4+4×5.2
length= 4+20.8=24.8m
Check
Perimeter of Rectangle=2( 24.8+5.2)
Perimeter of Rectangle=2(30)
Perimeter of Rectangle= 60m
Extra information=>
Perimeter is the total distance occupy by a solid 2D figure around its edge.
Area of Rectangle= length × breadth
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Concept:-
draw a rhombus and its diagonals
the diagonals bisect each other and are perpendicular to each other
the diagonals form four right triangles
choose one
the hypotenuse is one of the sides of the rhombus, 52 cm
Solution:-
(i) one leg of the triangle is 1/2 of 40 which is 20
the other leg, which is half of the other diagonal, is unknown so call it "d"
→522=202+d2
→2704=400+d2
→d2=2704-400
→d2=2304
→d=√2304
d=48 cm
therefore, the other diagonal is 2*48=96 cm
(ii) the formula for the area of a rhombus is...
A=(1/2)×diagonal1×diagonal2
A=(1/2)×40×96
A=20×96
A=1920 sq cm for the area of the rhombus